Monodisperse Magnetite Nanoparticles with Nearly Ideal Saturation Magnetization

Total Page:16

File Type:pdf, Size:1020Kb

Monodisperse Magnetite Nanoparticles with Nearly Ideal Saturation Magnetization Electronic Supplementary Material (ESI) for RSC Advances. This journal is © The Royal Society of Chemistry 2016 Supporting Information for Monodisperse magnetite nanoparticles with nearly ideal saturation magnetization Scott J. Kemp, R. Matthew Ferguson, Amit P. Khandhar, and Kannan M. Krishnan*,† LodeSpin Labs, 225 Fluke Hall, 4000 Mason Road, Seattle, Washington 98195, USA. †Department of Materials Sciences & Engineering, Roberts Hall, University of Washington, Seattle, Washington 98195, USA. Iron oleate synthesis and effects of workup on nanoparticle morphology Upon scaling iron oxide nanoparticle synthesis from 2.5 to 40 mmol of iron per batch, we initially noticed large variations in the dispersity and morphology of the nanoparticles. In some cases cubes, rods, triangles and/or plates contaminated the resulting nanoparticles. Since each batch of iron oleate was used to perform multiple thermolysis runs, it soon became apparent that variations in the iron oleate synthesis protocol resulted in large differences in the morphology of the resulting nanoparticles. We initially had been synthesizing iron oleate at room temperature following a known procedure {Jana:2004kl} and the resulting solution of iron oleate in hexanes after extraction was concentrated by rotary evaporation at 50 °C using a house vacuum system over about an hour. Iron oleate prepared via this method typically gave good quality particles. When the concentration procedure was changed to evaporating the hexanes at 25 °C and 20 mmHg, the resulting iron oleate failed to produce quality nanoparticles. In order to better understand the effect of temperature and time on the viability of the iron oleate, several different iron oleate preparations were utilized and evaluated. Synthesis of iron oleate at room temperature for 4 hrs, 18 hrs or 65 hrs, followed by standard work-up and concentration at room temperature, all produced an iron oleate which gave poor particle morphology and/or size distribution. Evaluation of reflux (57 °C) conditions for 18 hrs produced solids during the work-up which complicated the extraction procedure. Iron oleate produced at reflux for 4 hrs followed by stirring at room temperature for 15 hrs decomposed to form good nanoparticles sometimes, but not consistently. When the reaction was stirred at room temperature for 16 hrs then heated at reflux for 4 hrs the resulting iron oleate gave very good particles. For thermolysis at 324 °C in octadecene, Iron oleate made using the conditions described in {Park:2004jf}, namely synthesis at reflux for 4 hours, followed by immediate work-up, routinely gave the most monodispersed Figure S1. Examples of nanoparticles resulting from nonoptimal iron oleate. nanoparticles, free of contaminating shapes. These results lead us to believe iron(III) oleate forms multiple structures, not all favorable for nanoparticle synthesis, and the preferred structure is formed upon heating at reflux, but slowly transforms to less desirable forms while stirring the reaction mixture at room temperature. It was also realized the iron oleate mixture contains incorporated water and/or ethanol and oleic acid (free or as ligands) and these components could fluctuate based on even small variations to the procedure, affecting the reproducibility of the resulting nanoparticle size. For example, when the iron oleate solution in hexane was dried with sodium sulfate, extending the drying time from 10 minutes to 45 minutes produced a thickened material which could no longer be gravity filtered. As a precaution, the synthesis of iron oleate was standardized and every aspect of the procedure was strictly adhered to in order to generate consistent batches of iron oleate. Size reproducibility and stirring control during the nanoparticle formation via thermolysis. One common problem with scaling up reactions is the change in heat transfer rates related to volume to surface area increase and stirring efficiency. In some instances, we observed side by side reactions with identical reaction mixtures result in different size outcomes. Even though the stir plates were the same model and both set to the same speed, it became apparent the stir plates often stirred at different rates. To confirm stir rate had a significant influence on the resulting size, two reactions were performed side by side (batch 9-156 and 9-157). During the heating and nucleation phases of the thermolysis, one reaction was stirred vigorously (~1000 rpm, such that the center of the stir bar was clearly visible in the bottom of the vortex (~5 cm deep)) and a second reaction was stirred much slower (~300 rpm, the vortex in the center of the reaction was only 1 cm deep). The resulting nanoparticles had a large difference in median diameter: 27.4 nm (sigma = 0.07) for the fast stir rate and 35.9 nm (sigma = 0.08) for the slow stir rate. This dramatic difference in size clearly indicated stirring control is critical to obtain size reproducibility. TLC Analysis of thermolysis reaction mixture for oleic acid ketonization by- product and isolation of fatty ketones. In order to determine the extent of ketonization during a thermolysis reaction the following procedure was used: Technical grade oleic acid (90%) was used. A standard thermolysis reaction was perform on 40 mmol of Fe using 7.2:1 oleic acid ratio and halting the reaction 1 hr after the turbidity event. From this reaction mixture a 10 mL sample (about 1/37th of the total) was taken. The black solution was diluted with heptane (10 mL), ethyl acetate (20 mL) and acetone (3 mL) and centrifuged to remove the iron oxide nanoparticles. The resulting supernatant solution was concentrated on a rotary evaporator. The material was evaluated by TLC (MerckKGaA TLC Silica gel 60 F254) along with standards of oleic acid and octadecene using dichloromethane/hexanes (1:1) as eluent: TLC showed a pair of high Rf spots determined to be octadecane (Rf = 0.85) and octadecene (Rf = 0.81), followed by the fatty ketones as a mixture of possible products (Rf = 0.64 to 0.36, major spot at 0.43) and traces of unknowns near the baseline. To quantify the amount of ketones in the sample, the material was eluted through silicagel (200 mL) with hexanes (~200 mL) to elute the octadecene and octadecane. The silicagel was then eluted with dichloromethane (~500 mL) which eluted the ketone products. All fractions containing ketones, as determined by TLC analysis, were rechromatographed using dichloromethane/hexanes (1:1) to give a mixture of ketones (2.261 grams). The ketone material was verified by 1 H NMR (300 MHz, DCCl3) see Figure S3. Additional experimental procedures. Synthesis of Iron(III) oleate as a solution in 1-octadecene. In some cases for ease of transfer it was desireable to maintain iron oleate as a solution in 1-octadecene. The standard procedure from the publication was modified in the following way: During the work-up, when evaporation of hexane had slowed, 1-octadecene (200 mL) was added and concentrating was continued on a rotary evaporator with high vacuum for about 30 minutes. The iron(III) oleate solution was placed on a high vacuum line overnight. The resulting solution was deemed to contain 160 mmol of iron(III) and 1-octadecene (200 mL) and could be divided by mass for use in the nanoparticle synthesis. TEM analysis of Iron oxide Nanoparticles. A sample for TEM was prepared with 2 mL of reaction mixture added to a 40 mL vial, followed by the addition of hexanes (3 mL) followed by the addition of ethyl acetate (10 mL). The vial was placed on the edge of a FeNdB permanent magnet, Grade N51 (3” x 3” x 1”) for about 10 minutes. The solution was removed from the resulting black solids and the wash procedure was repeated 2 more times. The black nanoparticles (about 10 mg) were dissolved in chloroform (about 2mL), sonicated for a few minutes and 10 microliters of the solution were added, in 3-4 drops from a 10 microliter pipette, to a TEM grid (pure carbon film on 200 mesh copper grid, Ted Pella catalog number 01840-F) for TEM imaging and electron diffraction. TEM size was determined from bright field images acquired with a FEI Technai G2 F20 at 200 kV. Multiple micrographs were analyzed, typically > 3 images acquired from different regions of the grid, with >1000 particles total. Diameter histograms were generated using the particle size analyzer (PSA r12) plugin available for the Imagej software and the results were fit to a log-normal distribution function using Mathematica. Selected area electron diffraction (SAED) patterns were analyzed using the radial integration tool in imagej. Magnetic Characterization by vibrating sample Magnetometer (VSM). A 10 mg sample of washed iron oxide nanoparticles were coated with PMAO-PEG co-polymer and phase transferred into water for magnetic characterization. Magnetization versus field measurements were measured at room temperature in a VSM (LakeShore) with fields up to 0.2 T. Magnetic size was determined by fitting the MvH curves to a langevin function using Chantrell’s method. Samples contained 100 microliters of nanoparticle-DI water suspension at a typical concentration of 2 g Fe/L. Iron oxide Nanoparticle washing procedure. A portion of the crude reaction mixture containing nanoparticles (10 mL) was washed by the addition of ethyl acetate (30 mL). The vial was placed on the edge of a FeNdB permanent magnet, Grade N51 (3” x 3” x 1”) for about 10 minutes. The solution was removed from the resulting black solids and the solids were dissolved in heptane (5 mL) with sonication. Ethyl acetate (20 mL) was added and the magnetic separation was repeated. The washing procedure was repeated an additional 2 times. After the last wash, the iron oxide cores were dried under high vacuum for at least 30 minutes to give about 60 mg of iron oxide nanoparticles.
Recommended publications
  • Selecting the Optimal Inductor for Power Converter Applications
    Selecting the Optimal Inductor for Power Converter Applications BACKGROUND SDR Series Power Inductors Today’s electronic devices have become increasingly power hungry and are operating at SMD Non-shielded higher switching frequencies, starving for speed and shrinking in size as never before. Inductors are a fundamental element in the voltage regulator topology, and virtually every circuit that regulates power in automobiles, industrial and consumer electronics, SRN Series Power Inductors and DC-DC converters requires an inductor. Conventional inductor technology has SMD Semi-shielded been falling behind in meeting the high performance demand of these advanced electronic devices. As a result, Bourns has developed several inductor models with rated DC current up to 60 A to meet the challenges of the market. SRP Series Power Inductors SMD High Current, Shielded Especially given the myriad of choices for inductors currently available, properly selecting an inductor for a power converter is not always a simple task for designers of next-generation applications. Beginning with the basic physics behind inductor SRR Series Power Inductors operations, a designer must determine the ideal inductor based on radiation, current SMD Shielded rating, core material, core loss, temperature, and saturation current. This white paper will outline these considerations and provide examples that illustrate the role SRU Series Power Inductors each of these factors plays in choosing the best inductor for a circuit. The paper also SMD Shielded will describe the options available for various applications with special emphasis on new cutting edge inductor product trends from Bourns that offer advantages in performance, size, and ease of design modification.
    [Show full text]
  • Magnetic Materials: Hysteresis
    Magnetic Materials: Hysteresis Ferromagnetic and ferrimagnetic materials have non-linear initial magnetisation curves (i.e. the dotted lines in figure 7), as the changing magnetisation with applied field is due to a change in the magnetic domain structure. These materials also show hysteresis and the magnetisation does not return to zero after the application of a magnetic field. Figure 7 shows a typical hysteresis loop; the two loops represent the same data, however, the blue loop is the polarisation (J = µoM = B-µoH) and the red loop is the induction, both plotted against the applied field. Figure 7: A typical hysteresis loop for a ferro- or ferri- magnetic material. Illustrated in the first quadrant of the loop is the initial magnetisation curve (dotted line), which shows the increase in polarisation (and induction) on the application of a field to an unmagnetised sample. In the first quadrant the polarisation and applied field are both positive, i.e. they are in the same direction. The polarisation increases initially by the growth of favourably oriented domains, which will be magnetised in the easy direction of the crystal. When the polarisation can increase no further by the growth of domains, the direction of magnetisation of the domains then rotates away from the easy axis to align with the field. When all of the domains have fully aligned with the applied field saturation is reached and the polarisation can increase no further. If the field is removed the polarisation returns along the solid red line to the y-axis (i.e. H=0), and the domains will return to their easy direction of magnetisation, resulting in a decrease in polarisation.
    [Show full text]
  • Assignment 3
    PHYSICS 2800 – 2nd TERM Introduction to Materials Science Assignment 3 Date of distribution: Tuesday, March 9, 2010 Date for solutions to be handed in: Tuesday, March 16, 2010 -7 2 You may assume the standard values µ0 = 4 π × 10 kg-m/C for the permeability of vacuum -24 2 and µB = 9.27 × 10 A-m for the Bohr magneton. 3 1. Nickel is a ferromagnetic metal with density 8.90 g/cm . Given that Avogadro’s number NA = 6.02 × 10 23 atoms/mol and the atomic weight of Ni is 58.7, calculate the number of atoms of Ni per cubic metre. If one atom of Ni has a magnetic moment of 0.6 Bohr magnetons, deduce the saturation magnetization Ms and the saturation magnetic induction Bs for Ni. Answer: 3 The saturation magnetization is given by Ms = 0.6 µBN , where N is the number of atoms/m . ρN A But N = , where ρ is the density and ANi is the atomic weight of Ni. ANi 90.8( ×10 6 g/m 3 )( 02.6 ×10 23 atoms/mol ) So N = = 9.13 × 10 28 atoms/m 3. 58 7. g/mol -24 28 5 Then Ms = 0.6 (9.27 × 10 )( 9.13 × 10 ) = 5.1 × 10 A/m. Finally (from the lecture notes), -7 5 BS = µ0MS = (4 π × 10 )(5.1 × 10 ) = 0.64 Tesla. 2. The magnetization within a bar of some metal alloy is 1.2 × 10 6 A/m when the H field is 200 A/m. Calculate (a) the magnetic susceptibility χm of this alloy, (b) the permeability µ, and (c) the magnetic induction B within the alloy.
    [Show full text]
  • Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets
    Basic design and engineering of normal-conducting, iron-dominated electromagnets Th. Zickler CERN, Geneva, Switzerland Abstract The intention of this course is to provide guidance and tools necessary to carry out an analytical design of a simple accelerator magnet. Basic concepts and magnet types will be explained as well as important aspects which should be considered before starting the actual design phase. The central part of this course is dedicated to describing how to develop a basic magnet design. Subjects like the layout of the magnetic circuit, the excitation coils, and the cooling circuits will be discussed. A short introduction to materials for the yoke and coil construction and a brief summary about cost estimates for magnets will complete this topic. 1 Introduction The scope of these lectures is to give an overview of electromagnetic technology as used in and around particle accelerators considering normal-conducting, iron-dominated electromagnets generally restricted to direct current situations where we assume that the voltages generated by the change of flux and possible resulting eddy currents are negligible. Permanent and superconducting magnet technologies as well as special magnets like kickers and septa are not covered in this paper; they were part of dedicated special lectures. It is clear that it is difficult to give a complete and exhaustive summary of magnet design since there are many different magnet types and designs; in principle the design of a magnet is limited only by the laws of physics and the imagination of the magnet designer. Furthermore, each laboratory and each magnet designer or engineer has his own style of approaching a particular magnet design.
    [Show full text]
  • Magnetic Materials: Soft Magnets
    Magnetic Materials: Soft Magnets Soft magnetic materials are those materials that are easily magnetised and demagnetised. They typically have intrinsic coercivity less than 1000 Am-1. They are used primarily to enhance and/or channel the flux produced by an electric current. The main parameter, often used as a figure of merit for soft magnetic materials, is the relative permeability (µr, where µr = B/ µoH), which is a measure of how readily the material responds to the applied magnetic field. The other main parameters of interest are the coercivity, the saturation magnetisation and the electrical conductivity. The types of applications for soft magnetic materials fall into two main categories: AC and DC. In DC applications the material is magnetised in order to perform an operation and then demagnetised at the conclusion of the operation, e.g. an electromagnet on a crane at a scrap yard will be switched on to attract the scrap steel and then switched off to drop the steel. In AC applications the material will be continuously cycled from being magnetised in one direction to the other, throughout the period of operation, e.g. a power supply transformer. A high permeability will be desirable for each type of application but the significance of the other properties varies. For DC applications the main consideration for material selection is most likely to be the permeability. This would be the case, for example, in shielding applications where the flux must be channelled through the material. Where the material is used to generate a magnetic field or to create a force then the saturation magnetisation may also be significant.
    [Show full text]
  • Vocabulary of Magnetism
    TECHNotes The Vocabulary of Magnetism Symbols for key magnetic parameters continue to maximum energy point and the value of B•H at represent a challenge: they are changing and vary this point is the maximum energy product. (You by author, country and company. Here are a few may have noticed that typing the parentheses equivalent symbols for selected parameters. for (BH)MAX conveniently avoids autocorrecting Subscripts in symbols are often ignored so as to the two sequential capital letters). Units of simplify writing and typing. The subscripted letters maximum energy product are kilojoules per are sometimes capital letters to be more legible. In cubic meter, kJ/m3 (SI) and megagauss•oersted, ASTM documents, symbols are italicized. According MGOe (cgs). to NIST’s guide for the use of SI, symbols are not italicized. IEC uses italics for the main part of the • µr = µrec = µ(rec) = recoil permeability is symbol, but not for the subscripts. I have not used measured on the normal curve. It has also been italics in the following definitions. For additional called relative recoil permeability. When information the reader is directed to ASTM A340[11] referring to the corresponding slope on the and the NIST Guide to the use of SI[12]. Be sure to intrinsic curve it is called the intrinsic recoil read the latest edition of ASTM A340 as it is permeability. In the cgs-Gaussian system where undergoing continual updating to be made 1 gauss equals 1 oersted, the intrinsic recoil consistent with industry, NIST and IEC usage. equals the normal recoil minus 1.
    [Show full text]
  • Glossary of MRI Terms A
    Glossary of MRI Terms A Absorption mode. Component of the MR signal that yields a symmetric, positive-valued line shape. Acceleration factor. The multiplicative term by which faster imaging pulse sequences such as multiple echo imaging reduce total imaging time compared to conventional imaging sequences such as spin echo imaging. Acoustic noise. Vibrations of the gradient coil support structures create sound waves. These vibrations are caused by interactions of the magnetic field created by pulses of the current through the gradient coil with the main magnetic field in a manner similar to a loudspeaker coil. Sound pressure is reported on a logarithmic scale called sound-pressure level expressed in decibels (dB) referenced to the weakest audible 1,000 Hz sound pressure of 2x10–5 pascal. Sound level meters contain filters that simulate the ear’s frequency response. The most commonly used filter provides what is called A weighting, with the letter A appended to the dB units, i.e., dBA. Acquisition matrix. Number of independent data samples in each direction, e.g., in 2DFT imaging it is the number of samples in the phase-encoding and frequency-encoding directions, and in reconstruction from projections imaging it is the number of samples in time and angle. The acquisition matrix may be asymmetric and of different size than the reconstructed image or display matrix, e.g., with zero filling or interpolation, or (for asymmetric sampling) by exploiting the symmetry of the data matrix. For symmetric sampling, the acquisition matrix will roughly equal the ratio of image field of view to spatial resolution along the corresponding direction (depending on filtering and other processing).
    [Show full text]
  • Tuning Structural and Magnetic Properties of Fe Oxide Nanoparticles by Specifc Hydrogenation Treatments S
    www.nature.com/scientificreports OPEN Tuning structural and magnetic properties of Fe oxide nanoparticles by specifc hydrogenation treatments S. G. Greculeasa1, P. Palade1, G. Schinteie1, A. Leca1, F. Dumitrache2, I. Lungu2, G. Prodan3, A. Kuncser1 & V. Kuncser1* Structural and magnetic properties of Fe oxide nanoparticles prepared by laser pyrolysis and annealed in high pressure hydrogen atmosphere were investigated. The annealing treatments were performed at 200 °C (sample A200C) and 300 °C (sample A300C). The as prepared sample, A, consists of nanoparticles with ~ 4 nm mean particle size and contains C (~ 11 at.%), Fe and O. The Fe/O ratio is between γ-Fe2O3 and Fe3O4 stoichiometric ratios. A change in the oxidation state, crystallinity and particle size is evidenced for the nanoparticles in sample A200C. The Fe oxide nanoparticles are completely reduced in sample A300C to α-Fe single phase. The blocking temperature increases from 106 K in A to 110 K in A200C and above room temperature in A300C, where strong inter-particle interactions are evidenced. Magnetic parameters, of interest for applications, have been considerably varied by the specifc hydrogenation treatments, in direct connection to the induced specifc changes of particle size, crystallinity and phase composition. For the A and A200C samples, a feld cooling dependent unidirectional anisotropy was observed especially at low temperatures, supporting the presence of nanoparticles with core–shell-like structures. Surprisingly high MS values, almost 50% higher than for bulk metallic Fe, were evidenced in sample A300C. Fe-based nanoparticles (NPs) show remarkable interest in the scientifc community for various applications such as biomedicine (hyperthermia1, targeted drug delivery2, computed tomography and magnetic resonance imaging contrast agents3,4), catalysis5,6, magnetic fuids7, gas sensors8, high-density magnetic storages 9, water treatment and environment protection 10,11.
    [Show full text]
  • Electromagnetic Fields and Energy
    MIT OpenCourseWare http://ocw.mit.edu Haus, Hermann A., and James R. Melcher. Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall, 1989. ISBN: 9780132490207. Please use the following citation format: Haus, Hermann A., and James R. Melcher, Electromagnetic Fields and Energy. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed [Date]). License: Creative Commons Attribution-NonCommercial-Share Alike. Also available from Prentice-Hall: Englewood Cliffs, NJ, 1989. ISBN: 9780132490207. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms 9 MAGNETIZATION 9.0 INTRODUCTION The sources of the magnetic fields considered in Chap. 8 were conduction currents associated with the motion of unpaired charge carriers through materials. Typically, the current was in a metal and the carriers were conduction electrons. In this chapter, we recognize that materials provide still other magnetic field sources. These account for the fields of permanent magnets and for the increase in inductance produced in a coil by insertion of a magnetizable material. Magnetization effects are due to the propensity of the atomic constituents of matter to behave as magnetic dipoles. It is natural to think of electrons circulating around a nucleus as comprising a circulating current, and hence giving rise to a magnetic moment similar to that for a current loop, as discussed in Example 8.3.2. More surprising is the magnetic dipole moment found for individual electrons. This moment, associated with the electronic property of spin, is defined as the Bohr magneton e 1 m = ± ¯h (1) e m 2 11 where e/m is the electronic charge­to­mass ratio, 1.76 × 10 coulomb/kg, and 2π¯h −34 2 is Planck’s constant, ¯h = 1.05 × 10 joule­sec so that me has the units A − m .
    [Show full text]
  • Physics and Measurements of Magnetic Materials
    Physics and measurements of magnetic materials S. Sgobba CERN, Geneva, Switzerland Abstract Magnetic materials, both hard and soft, are used extensively in several components of particle accelerators. Magnetically soft iron–nickel alloys are used as shields for the vacuum chambers of accelerator injection and extraction septa; Fe-based material is widely employed for cores of accelerator and experiment magnets; soft spinel ferrites are used in collimators to damp trapped modes; innovative materials such as amorphous or nanocrystalline core materials are envisaged in transformers for high- frequency polyphase resonant convertors for application to the International Linear Collider (ILC). In the field of fusion, for induction cores of the linac of heavy-ion inertial fusion energy accelerators, based on induction accelerators requiring some 107 kg of magnetic materials, nanocrystalline materials would show the best performance in terms of core losses for magnetization rates as high as 105 T/s to 107 T/s. After a review of the magnetic properties of materials and the different types of magnetic behaviour, this paper deals with metallurgical aspects of magnetism. The influence of the metallurgy and metalworking processes of materials on their microstructure and magnetic properties is studied for different categories of soft magnetic materials relevant for accelerator technology. Their metallurgy is extensively treated. Innovative materials such as iron powder core materials, amorphous and nanocrystalline materials are also studied. A section considers the measurement, both destructive and non-destructive, of magnetic properties. Finally, a section discusses magnetic lag effects. 1 Magnetic properties of materials: types of magnetic behaviour The sense of the word ‘lodestone’ (waystone) as magnetic oxide of iron (magnetite, Fe3O4) is from 1515, while the old name ‘lodestar’ for the pole star, as the star leading the way in navigation, is from 1374.
    [Show full text]
  • Residual Magnetism
    Residual Magnetism Will Knapek 23 January 2012 AGENDA > What is Residual Magnetism > Ways to Reduce Remanence > Determining the residual magnetism in a field test > Summary Page 2 Significance of Residual Magnetism It has been said that one really knows very little about a problem until it can be reduced to figures. One may or may not need to demagnetize, but until one actually measures residual levels of magnetism, one really doesn’t know where he or she is. One has not reduced the problem to figures. R. B. Annis Instruments, Notes on Demagnetizing 3 Physical Interpretation of Residual Magnetism • When excitation is removed from the CT, some of the magnetic domains retain a degree of orientation relative to the magnetic field that was applied to the core. This phenomenon is known as residual magnetism. • Residual magnetism in CTs can be quantitatively described by amount of flux stored in the core. t (t) V ( )d C res 0 Significance of Residual Magnetism WHY DO I CARE???? Bottom Line: If the CT has excessive Residual Magnetism, it will saturate sooner than expected. 5 Magnetization Process and Hysteresis *Picture is reproduced from K. Demirchyan et.al., Theoretical Foundations of Electrotechnics Remanence Flux (Residual Magnetism) When excitation stops, Flux does not go to zero Remanence is dissipated very little under service conditions. Demagnetization is required to remove the remanence. *Source: IEEE C37.100-2007 © OMICRON Page 7 Residual Remanence and Remanence Factor • Saturation flux (Ψs) that peak value of the flux which would
    [Show full text]
  • Chapter 7 Micromagnetism, Domains and Hysteresis
    Chapter 7 Micromagnetism, domains and hysteresis 7.1 Micromagnetic energy 7.2 Domain theory 7.5 Reversal, pinning and nucleation TCD March 2007 1 The hysteresis loop spontaneous magnetization remanence coercivity virgin curve initial susceptibility major loop The hysteresis loop shows the irreversible, nonlinear response of a ferromagnet to a magnetic field . It reflects the arrangement of the magnetization in ferromagnetic domains. The magnet cannot be in thermodynamic equilibrium anywhere around the open part of the curve! M and H have the same units (A m-1). TCD March 2007 2 Domains form to minimize the dipolar energy Ed TCD March 2007 3 TCD March 2007 4 Magnetostatics Poisson’s equarion Volume charge Boundary condition en 2. air + 1. solid + M + M( r) ! H( r) BUT H( r) ! M( r) Experimental information about the domain structure comes from observations at the surface. The interior is inscruatble. TCD March 2007 5 7.1 Micromagnetic energy TCD March 2007 6 1.1 Exchange eM = M( r)/Ms (",#) Exchange length A = kTC/2a 2 A = 2JS Zc/a0 A ~ 10 pJ m-1 Lex ~ 2 - 3 nm Exchange energy of vortex 2 $Eex = JS ln (R/a) TCD March 2007 7 1.2 Anisotropy 2 2 7 -3 EK = K1sin " Bulk K1 ~ 10 - 10 J m -2 Surface Ksa ~ 0.1 - 1 mJ m . -2 Interface Kea ~ 1 mJ m . Exchange and anisotropy govern the width of the domain wall. TCD March 2007 8 1.3 Demagnetizing field Demagnetizing field governs the formation of the wall (integral over all space) and B = µ0(H + M) Hd is determined by the volume and surface charge distributions %.M and en.M 2 &m = qm/4'r; % &m= -(m H = - %&m TCD March 2007 9 1.4 Stress Magnetoelastic strain tensor For isotropic material, uniaxial stress Induced uniaxial anisotropy TCD March 2007 10 1.5 Magnetosriction Local stresses can be created by the magnetostriction of the ferromagnet itself: Magnetostrictive stress Deviation due to magnetostriction Elastic tensor Usually this term is small < 1 kj m-3 , but it can influence the formation of closure domains.
    [Show full text]